Abstract

We put forward the existence of localized necklace solitons and ring solitons in a defocusing cubic nonlinear medium with an imprinted Bessel optical lattice. Novel families of necklace solitons are found and their unique properties, including multistable states are revealed. We show that both necklace solitons and ring solitons could reside on any ring of the Bessel lattices. They are dynamically stable provided that the lattice is modulated deep enough. The uncovered phenomena may open a new way for soliton control and manipulation.

© 2008 Optical Society of America

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  1. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, San Diego,Calif., 2003).
  2. Y. Silberberg and G. I. Stegeman, Spatial Solitons (Springer, New York, 2001).
  3. A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical Vortices and Vortex Solitons,” Prog. Opt. 47, 291 (2005).
    [Crossref]
  4. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature (London)  422, 147 (2003).
    [Crossref] [PubMed]
  5. D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of Discrete Vortex Solitons in Optically Induced Photonic Lattices,” Phys. Rev. Lett. 92, 123 903 (2004).
    [Crossref]
  6. J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, “Observation of Vortex Lattices in Bose-Einstein Condensates,” Science 292, 476 (2001).
    [Crossref] [PubMed]
  7. O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hnsch, and I. Bloch, “Controlled collisions for multi-particle entanglement of optically trapped atoms,” Nature 425, 937 (2003).
    [Crossref] [PubMed]
  8. K. Motzek, A. A. Sukhorukov, and Y. S. Kivshar, “Polychromatic interface solitons in nonlinear photonic lattices,” Opt. Lett. 31, 3125 (2006).
    [Crossref] [PubMed]
  9. X. Wang, Z. Chen, and P. G. Kevrekidis, “Observation of Discrete Solitons and Soliton Rotation in Optically Induced Periodic Ring Lattices,” Phys. Rev. Lett. 96, 083 904 (2006).
  10. J. Yang, “Stability of vortex solitons in a photorefractive optical lattice,” N. J. Phys. 6, 47 (2004).
    [Crossref]
  11. J. Yang and Z. H. Musslimani, “Fundamental and vortex solitons in a two-dimensional optical lattice,” Opt. Lett. 28, 2094 (2003).
    [Crossref] [PubMed]
  12. J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297 (2000).
    [Crossref]
  13. A. Vasara, J. Turunen, and A. Friberg, “Realization of General Nondiffracting Beams with Computer-generated holograms,” J. Opt. Soc. Am. A 6, 1748 (1989).
    [Crossref] [PubMed]
  14. Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, “Soliton Topology versus Discrete Symmetry in Optical Lattices,” Phys. Rev. Lett. 95, 123 902 (2005).
    [Crossref]
  15. R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, “Observation of light localization in modulated Bessel optical lattices,” Opt. Express 14, 2825 (2006).
    [Crossref] [PubMed]
  16. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable Ring-Profile Vortex Solitons in Bessel Optical Lattices,” Phys. Rev. Lett. 94, 043 902 (2005).
    [Crossref]
  17. Y. V. Kartashov, R. Carretero-González, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Multipole-mode solitons in Bessel optical lattices,” Opt. Express 13, 10 703 (2005).
    [Crossref]
  18. D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable Spatiotemporal Solitons in Bessel Optical Lattices,” Phys. Rev. Lett. 95, 023 902 (2005).
    [Crossref]
  19. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary Solitons in Bessel Optical Lattices,” Phys. Rev. Lett. 93, 093 904 (2004).
    [Crossref]
  20. Y. V. Kartashov, A. Egorov, V. Vysloukh, and L. Torner, “Rotary dipole-mode solitons in Bessel optical lattices,” J. Opt. B: Quantum Semiclass. Opt. 6, 444 (2004).
    [Crossref]
  21. X. Wang, Z. Chen, and J. Yang, “Guiding light in optically induced ring lattices with a low-refractive-index core,” Opt. Lett. 31, 1887 (2006).
    [Crossref] [PubMed]
  22. M. SoljaÇić, S. Sears, and M. Segev, “Self-Trapping of Necklace Beams in Self-Focusing Kerr Media,” Phys. Rev. Lett. 81, 4851 (1998).
    [Crossref]
  23. T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and Stability of Necklace Beams in Kerr Media,” Phys. Rev. Lett. 99, 133 902 (2007).
    [Crossref]
  24. A. S. Desyatnikov and Y. S. Kivshar, “Necklace-Ring Vector Solitons,” Phys. Rev. Lett. 87, 033 901 (2001).
    [Crossref]
  25. M. SoljaÇić and M. Segev, “Integer and Fractional Angular Momentum Borne on Self-Trapped Necklace-Ring Beams,” Phys. Rev. Lett. 86, 420 (2001).
    [Crossref] [PubMed]
  26. C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, and L. Torner, “Two-dimensional multipole solitons in nonlocal nonlinear media,” Opt. Lett. 31, 3312 (2006).
    [Crossref] [PubMed]
  27. Y. J. He, H. H. Fan, J. W. Dong, and H. Z. Wang, “Self-trapped spatiotemporal necklace-ring solitons in the Ginzburg-Landau equation,” Phys. Rev. E 74, 016 611 (2006).
    [Crossref]
  28. Y. Cai and S. He, “Propagation of various dark hollow beams in a turbulent atmosphere,” Opt. Express 14, 1353 (2006).
    [Crossref] [PubMed]
  29. J. Yin, W. Gao, and Y. Zhu, “Generation of dark hollow beams and their applications,” Prog. Opt. 45, 119 (2003).
    [Crossref]
  30. J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike Solitons in Optically Induced Photonic Lattices,” Phys. Rev. Lett. 94, 113 902 (2005).
    [Crossref]
  31. A. S. Desyatnikov and Y. S. Kivshar, “Rotating Optical Soliton Clusters,” Phys. Rev. Lett. 88, 053 901 (2002).
    [Crossref]
  32. Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, “Robust Propagation of Two-Color Soliton Clusters Supported by Competing Nonlinearities,” Phys. Rev. Lett. 89, 273 902 (2002).
    [Crossref]
  33. D. Mihalache, D. Mazilu, L.-C. Crasovan, B. A. Malomed, F. Lederer, and L. Torner, “Robust soliton clusters in media with competing cubic and quintic nonlinearities,” Phys. Rev. E 68, 046 612 (2003).
    [Crossref]
  34. L.-C. Crasovan, Y. V. Kartashov, D. Mihalache, L. Torner, Y. S. Kivshar, and V. M. Pérez-García, “Soliton molecules: Robust clusters of spatiotemporal optical solitons,” Phys. Rev. E 67, 046 610 (2003).
    [Crossref]

2007 (1)

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and Stability of Necklace Beams in Kerr Media,” Phys. Rev. Lett. 99, 133 902 (2007).
[Crossref]

2006 (7)

2005 (6)

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, “Soliton Topology versus Discrete Symmetry in Optical Lattices,” Phys. Rev. Lett. 95, 123 902 (2005).
[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable Ring-Profile Vortex Solitons in Bessel Optical Lattices,” Phys. Rev. Lett. 94, 043 902 (2005).
[Crossref]

Y. V. Kartashov, R. Carretero-González, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Multipole-mode solitons in Bessel optical lattices,” Opt. Express 13, 10 703 (2005).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable Spatiotemporal Solitons in Bessel Optical Lattices,” Phys. Rev. Lett. 95, 023 902 (2005).
[Crossref]

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical Vortices and Vortex Solitons,” Prog. Opt. 47, 291 (2005).
[Crossref]

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike Solitons in Optically Induced Photonic Lattices,” Phys. Rev. Lett. 94, 113 902 (2005).
[Crossref]

2004 (4)

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of Discrete Vortex Solitons in Optically Induced Photonic Lattices,” Phys. Rev. Lett. 92, 123 903 (2004).
[Crossref]

J. Yang, “Stability of vortex solitons in a photorefractive optical lattice,” N. J. Phys. 6, 47 (2004).
[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary Solitons in Bessel Optical Lattices,” Phys. Rev. Lett. 93, 093 904 (2004).
[Crossref]

Y. V. Kartashov, A. Egorov, V. Vysloukh, and L. Torner, “Rotary dipole-mode solitons in Bessel optical lattices,” J. Opt. B: Quantum Semiclass. Opt. 6, 444 (2004).
[Crossref]

2003 (6)

O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hnsch, and I. Bloch, “Controlled collisions for multi-particle entanglement of optically trapped atoms,” Nature 425, 937 (2003).
[Crossref] [PubMed]

J. Yang and Z. H. Musslimani, “Fundamental and vortex solitons in a two-dimensional optical lattice,” Opt. Lett. 28, 2094 (2003).
[Crossref] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature (London)  422, 147 (2003).
[Crossref] [PubMed]

J. Yin, W. Gao, and Y. Zhu, “Generation of dark hollow beams and their applications,” Prog. Opt. 45, 119 (2003).
[Crossref]

D. Mihalache, D. Mazilu, L.-C. Crasovan, B. A. Malomed, F. Lederer, and L. Torner, “Robust soliton clusters in media with competing cubic and quintic nonlinearities,” Phys. Rev. E 68, 046 612 (2003).
[Crossref]

L.-C. Crasovan, Y. V. Kartashov, D. Mihalache, L. Torner, Y. S. Kivshar, and V. M. Pérez-García, “Soliton molecules: Robust clusters of spatiotemporal optical solitons,” Phys. Rev. E 67, 046 610 (2003).
[Crossref]

2002 (2)

A. S. Desyatnikov and Y. S. Kivshar, “Rotating Optical Soliton Clusters,” Phys. Rev. Lett. 88, 053 901 (2002).
[Crossref]

Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, “Robust Propagation of Two-Color Soliton Clusters Supported by Competing Nonlinearities,” Phys. Rev. Lett. 89, 273 902 (2002).
[Crossref]

2001 (3)

A. S. Desyatnikov and Y. S. Kivshar, “Necklace-Ring Vector Solitons,” Phys. Rev. Lett. 87, 033 901 (2001).
[Crossref]

M. SoljaÇić and M. Segev, “Integer and Fractional Angular Momentum Borne on Self-Trapped Necklace-Ring Beams,” Phys. Rev. Lett. 86, 420 (2001).
[Crossref] [PubMed]

J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, “Observation of Vortex Lattices in Bose-Einstein Condensates,” Science 292, 476 (2001).
[Crossref] [PubMed]

2000 (1)

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297 (2000).
[Crossref]

1998 (1)

M. SoljaÇić, S. Sears, and M. Segev, “Self-Trapping of Necklace Beams in Self-Focusing Kerr Media,” Phys. Rev. Lett. 81, 4851 (1998).
[Crossref]

1989 (1)

Abo-Shaeer, J. R.

J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, “Observation of Vortex Lattices in Bose-Einstein Condensates,” Science 292, 476 (2001).
[Crossref] [PubMed]

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, San Diego,Calif., 2003).

Alexander, T. J.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of Discrete Vortex Solitons in Optically Induced Photonic Lattices,” Phys. Rev. Lett. 92, 123 903 (2004).
[Crossref]

Arlt, J.

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297 (2000).
[Crossref]

Bloch, I.

O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hnsch, and I. Bloch, “Controlled collisions for multi-particle entanglement of optically trapped atoms,” Nature 425, 937 (2003).
[Crossref] [PubMed]

Cai, Y.

Carretero-González, R.

Y. V. Kartashov, R. Carretero-González, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Multipole-mode solitons in Bessel optical lattices,” Opt. Express 13, 10 703 (2005).
[Crossref]

Chen, Z.

X. Wang, Z. Chen, and P. G. Kevrekidis, “Observation of Discrete Solitons and Soliton Rotation in Optically Induced Periodic Ring Lattices,” Phys. Rev. Lett. 96, 083 904 (2006).

X. Wang, Z. Chen, and J. Yang, “Guiding light in optically induced ring lattices with a low-refractive-index core,” Opt. Lett. 31, 1887 (2006).
[Crossref] [PubMed]

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike Solitons in Optically Induced Photonic Lattices,” Phys. Rev. Lett. 94, 113 902 (2005).
[Crossref]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of Discrete Vortex Solitons in Optically Induced Photonic Lattices,” Phys. Rev. Lett. 92, 123 903 (2004).
[Crossref]

Christodoulides, D. N.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature (London)  422, 147 (2003).
[Crossref] [PubMed]

Crasovan, L.-C.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable Spatiotemporal Solitons in Bessel Optical Lattices,” Phys. Rev. Lett. 95, 023 902 (2005).
[Crossref]

D. Mihalache, D. Mazilu, L.-C. Crasovan, B. A. Malomed, F. Lederer, and L. Torner, “Robust soliton clusters in media with competing cubic and quintic nonlinearities,” Phys. Rev. E 68, 046 612 (2003).
[Crossref]

L.-C. Crasovan, Y. V. Kartashov, D. Mihalache, L. Torner, Y. S. Kivshar, and V. M. Pérez-García, “Soliton molecules: Robust clusters of spatiotemporal optical solitons,” Phys. Rev. E 67, 046 610 (2003).
[Crossref]

Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, “Robust Propagation of Two-Color Soliton Clusters Supported by Competing Nonlinearities,” Phys. Rev. Lett. 89, 273 902 (2002).
[Crossref]

Desyatnikov, A. S.

R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, “Observation of light localization in modulated Bessel optical lattices,” Opt. Express 14, 2825 (2006).
[Crossref] [PubMed]

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical Vortices and Vortex Solitons,” Prog. Opt. 47, 291 (2005).
[Crossref]

A. S. Desyatnikov and Y. S. Kivshar, “Rotating Optical Soliton Clusters,” Phys. Rev. Lett. 88, 053 901 (2002).
[Crossref]

A. S. Desyatnikov and Y. S. Kivshar, “Necklace-Ring Vector Solitons,” Phys. Rev. Lett. 87, 033 901 (2001).
[Crossref]

Dholakia, K.

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297 (2000).
[Crossref]

Dong, J. W.

Y. J. He, H. H. Fan, J. W. Dong, and H. Z. Wang, “Self-trapped spatiotemporal necklace-ring solitons in the Ginzburg-Landau equation,” Phys. Rev. E 74, 016 611 (2006).
[Crossref]

Efremidis, N. K.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature (London)  422, 147 (2003).
[Crossref] [PubMed]

Egorov, A.

Y. V. Kartashov, A. Egorov, V. Vysloukh, and L. Torner, “Rotary dipole-mode solitons in Bessel optical lattices,” J. Opt. B: Quantum Semiclass. Opt. 6, 444 (2004).
[Crossref]

Egorov, A. A.

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, “Soliton Topology versus Discrete Symmetry in Optical Lattices,” Phys. Rev. Lett. 95, 123 902 (2005).
[Crossref]

Fan, H. H.

Y. J. He, H. H. Fan, J. W. Dong, and H. Z. Wang, “Self-trapped spatiotemporal necklace-ring solitons in the Ginzburg-Landau equation,” Phys. Rev. E 74, 016 611 (2006).
[Crossref]

Ferrando, A.

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, “Soliton Topology versus Discrete Symmetry in Optical Lattices,” Phys. Rev. Lett. 95, 123 902 (2005).
[Crossref]

Fischer, R.

Fleischer, J. W.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature (London)  422, 147 (2003).
[Crossref] [PubMed]

Frantzeskakis, D. J.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike Solitons in Optically Induced Photonic Lattices,” Phys. Rev. Lett. 94, 113 902 (2005).
[Crossref]

Friberg, A.

Gaeta, A. L.

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and Stability of Necklace Beams in Kerr Media,” Phys. Rev. Lett. 99, 133 902 (2007).
[Crossref]

Gao, W.

J. Yin, W. Gao, and Y. Zhu, “Generation of dark hollow beams and their applications,” Prog. Opt. 45, 119 (2003).
[Crossref]

Greiner, M.

O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hnsch, and I. Bloch, “Controlled collisions for multi-particle entanglement of optically trapped atoms,” Nature 425, 937 (2003).
[Crossref] [PubMed]

Grow, T. D.

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and Stability of Necklace Beams in Kerr Media,” Phys. Rev. Lett. 99, 133 902 (2007).
[Crossref]

He, S.

He, Y. J.

Y. J. He, H. H. Fan, J. W. Dong, and H. Z. Wang, “Self-trapped spatiotemporal necklace-ring solitons in the Ginzburg-Landau equation,” Phys. Rev. E 74, 016 611 (2006).
[Crossref]

Hnsch, T. W.

O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hnsch, and I. Bloch, “Controlled collisions for multi-particle entanglement of optically trapped atoms,” Nature 425, 937 (2003).
[Crossref] [PubMed]

Ishaaya, A. A.

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and Stability of Necklace Beams in Kerr Media,” Phys. Rev. Lett. 99, 133 902 (2007).
[Crossref]

Kartashov, Y. V.

C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, and L. Torner, “Two-dimensional multipole solitons in nonlocal nonlinear media,” Opt. Lett. 31, 3312 (2006).
[Crossref] [PubMed]

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, “Soliton Topology versus Discrete Symmetry in Optical Lattices,” Phys. Rev. Lett. 95, 123 902 (2005).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable Spatiotemporal Solitons in Bessel Optical Lattices,” Phys. Rev. Lett. 95, 023 902 (2005).
[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable Ring-Profile Vortex Solitons in Bessel Optical Lattices,” Phys. Rev. Lett. 94, 043 902 (2005).
[Crossref]

Y. V. Kartashov, R. Carretero-González, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Multipole-mode solitons in Bessel optical lattices,” Opt. Express 13, 10 703 (2005).
[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary Solitons in Bessel Optical Lattices,” Phys. Rev. Lett. 93, 093 904 (2004).
[Crossref]

Y. V. Kartashov, A. Egorov, V. Vysloukh, and L. Torner, “Rotary dipole-mode solitons in Bessel optical lattices,” J. Opt. B: Quantum Semiclass. Opt. 6, 444 (2004).
[Crossref]

L.-C. Crasovan, Y. V. Kartashov, D. Mihalache, L. Torner, Y. S. Kivshar, and V. M. Pérez-García, “Soliton molecules: Robust clusters of spatiotemporal optical solitons,” Phys. Rev. E 67, 046 610 (2003).
[Crossref]

Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, “Robust Propagation of Two-Color Soliton Clusters Supported by Competing Nonlinearities,” Phys. Rev. Lett. 89, 273 902 (2002).
[Crossref]

Ketterle, W.

J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, “Observation of Vortex Lattices in Bose-Einstein Condensates,” Science 292, 476 (2001).
[Crossref] [PubMed]

Kevrekidis, P. G.

X. Wang, Z. Chen, and P. G. Kevrekidis, “Observation of Discrete Solitons and Soliton Rotation in Optically Induced Periodic Ring Lattices,” Phys. Rev. Lett. 96, 083 904 (2006).

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike Solitons in Optically Induced Photonic Lattices,” Phys. Rev. Lett. 94, 113 902 (2005).
[Crossref]

Kivshar, Y. S.

K. Motzek, A. A. Sukhorukov, and Y. S. Kivshar, “Polychromatic interface solitons in nonlinear photonic lattices,” Opt. Lett. 31, 3125 (2006).
[Crossref] [PubMed]

R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, “Observation of light localization in modulated Bessel optical lattices,” Opt. Express 14, 2825 (2006).
[Crossref] [PubMed]

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical Vortices and Vortex Solitons,” Prog. Opt. 47, 291 (2005).
[Crossref]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of Discrete Vortex Solitons in Optically Induced Photonic Lattices,” Phys. Rev. Lett. 92, 123 903 (2004).
[Crossref]

L.-C. Crasovan, Y. V. Kartashov, D. Mihalache, L. Torner, Y. S. Kivshar, and V. M. Pérez-García, “Soliton molecules: Robust clusters of spatiotemporal optical solitons,” Phys. Rev. E 67, 046 610 (2003).
[Crossref]

A. S. Desyatnikov and Y. S. Kivshar, “Rotating Optical Soliton Clusters,” Phys. Rev. Lett. 88, 053 901 (2002).
[Crossref]

A. S. Desyatnikov and Y. S. Kivshar, “Necklace-Ring Vector Solitons,” Phys. Rev. Lett. 87, 033 901 (2001).
[Crossref]

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, San Diego,Calif., 2003).

Krolikowski, W.

Lederer, F.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable Spatiotemporal Solitons in Bessel Optical Lattices,” Phys. Rev. Lett. 95, 023 902 (2005).
[Crossref]

D. Mihalache, D. Mazilu, L.-C. Crasovan, B. A. Malomed, F. Lederer, and L. Torner, “Robust soliton clusters in media with competing cubic and quintic nonlinearities,” Phys. Rev. E 68, 046 612 (2003).
[Crossref]

Lopez-Aguayo, S.

Makasyuk, I.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike Solitons in Optically Induced Photonic Lattices,” Phys. Rev. Lett. 94, 113 902 (2005).
[Crossref]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of Discrete Vortex Solitons in Optically Induced Photonic Lattices,” Phys. Rev. Lett. 92, 123 903 (2004).
[Crossref]

Malomed, B. A.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable Spatiotemporal Solitons in Bessel Optical Lattices,” Phys. Rev. Lett. 95, 023 902 (2005).
[Crossref]

Y. V. Kartashov, R. Carretero-González, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Multipole-mode solitons in Bessel optical lattices,” Opt. Express 13, 10 703 (2005).
[Crossref]

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike Solitons in Optically Induced Photonic Lattices,” Phys. Rev. Lett. 94, 113 902 (2005).
[Crossref]

D. Mihalache, D. Mazilu, L.-C. Crasovan, B. A. Malomed, F. Lederer, and L. Torner, “Robust soliton clusters in media with competing cubic and quintic nonlinearities,” Phys. Rev. E 68, 046 612 (2003).
[Crossref]

Mandel, O.

O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hnsch, and I. Bloch, “Controlled collisions for multi-particle entanglement of optically trapped atoms,” Nature 425, 937 (2003).
[Crossref] [PubMed]

Martin, H.

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike Solitons in Optically Induced Photonic Lattices,” Phys. Rev. Lett. 94, 113 902 (2005).
[Crossref]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of Discrete Vortex Solitons in Optically Induced Photonic Lattices,” Phys. Rev. Lett. 92, 123 903 (2004).
[Crossref]

Mazilu, D.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable Spatiotemporal Solitons in Bessel Optical Lattices,” Phys. Rev. Lett. 95, 023 902 (2005).
[Crossref]

D. Mihalache, D. Mazilu, L.-C. Crasovan, B. A. Malomed, F. Lederer, and L. Torner, “Robust soliton clusters in media with competing cubic and quintic nonlinearities,” Phys. Rev. E 68, 046 612 (2003).
[Crossref]

Mihalache, D.

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable Spatiotemporal Solitons in Bessel Optical Lattices,” Phys. Rev. Lett. 95, 023 902 (2005).
[Crossref]

D. Mihalache, D. Mazilu, L.-C. Crasovan, B. A. Malomed, F. Lederer, and L. Torner, “Robust soliton clusters in media with competing cubic and quintic nonlinearities,” Phys. Rev. E 68, 046 612 (2003).
[Crossref]

L.-C. Crasovan, Y. V. Kartashov, D. Mihalache, L. Torner, Y. S. Kivshar, and V. M. Pérez-García, “Soliton molecules: Robust clusters of spatiotemporal optical solitons,” Phys. Rev. E 67, 046 610 (2003).
[Crossref]

Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, “Robust Propagation of Two-Color Soliton Clusters Supported by Competing Nonlinearities,” Phys. Rev. Lett. 89, 273 902 (2002).
[Crossref]

Motzek, K.

Musslimani, Z. H.

Neshev, D. N.

R. Fischer, D. N. Neshev, S. Lopez-Aguayo, A. S. Desyatnikov, A. A. Sukhorukov, W. Krolikowski, and Y. S. Kivshar, “Observation of light localization in modulated Bessel optical lattices,” Opt. Express 14, 2825 (2006).
[Crossref] [PubMed]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of Discrete Vortex Solitons in Optically Induced Photonic Lattices,” Phys. Rev. Lett. 92, 123 903 (2004).
[Crossref]

Ostrovskaya, E. A.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of Discrete Vortex Solitons in Optically Induced Photonic Lattices,” Phys. Rev. Lett. 92, 123 903 (2004).
[Crossref]

Pérez-García, V. M.

L.-C. Crasovan, Y. V. Kartashov, D. Mihalache, L. Torner, Y. S. Kivshar, and V. M. Pérez-García, “Soliton molecules: Robust clusters of spatiotemporal optical solitons,” Phys. Rev. E 67, 046 610 (2003).
[Crossref]

Raman, C.

J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, “Observation of Vortex Lattices in Bose-Einstein Condensates,” Science 292, 476 (2001).
[Crossref] [PubMed]

Rom, T.

O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hnsch, and I. Bloch, “Controlled collisions for multi-particle entanglement of optically trapped atoms,” Nature 425, 937 (2003).
[Crossref] [PubMed]

Rotschild, C.

Sears, S.

M. SoljaÇić, S. Sears, and M. Segev, “Self-Trapping of Necklace Beams in Self-Focusing Kerr Media,” Phys. Rev. Lett. 81, 4851 (1998).
[Crossref]

Segev, M.

C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, and L. Torner, “Two-dimensional multipole solitons in nonlocal nonlinear media,” Opt. Lett. 31, 3312 (2006).
[Crossref] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature (London)  422, 147 (2003).
[Crossref] [PubMed]

M. SoljaÇić and M. Segev, “Integer and Fractional Angular Momentum Borne on Self-Trapped Necklace-Ring Beams,” Phys. Rev. Lett. 86, 420 (2001).
[Crossref] [PubMed]

M. SoljaÇić, S. Sears, and M. Segev, “Self-Trapping of Necklace Beams in Self-Focusing Kerr Media,” Phys. Rev. Lett. 81, 4851 (1998).
[Crossref]

Silberberg, Y.

Y. Silberberg and G. I. Stegeman, Spatial Solitons (Springer, New York, 2001).

SoljaÇic, M.

M. SoljaÇić and M. Segev, “Integer and Fractional Angular Momentum Borne on Self-Trapped Necklace-Ring Beams,” Phys. Rev. Lett. 86, 420 (2001).
[Crossref] [PubMed]

M. SoljaÇić, S. Sears, and M. Segev, “Self-Trapping of Necklace Beams in Self-Focusing Kerr Media,” Phys. Rev. Lett. 81, 4851 (1998).
[Crossref]

Stegeman, G. I.

Y. Silberberg and G. I. Stegeman, Spatial Solitons (Springer, New York, 2001).

Sukhorukov, A. A.

Torner, L.

C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, and L. Torner, “Two-dimensional multipole solitons in nonlocal nonlinear media,” Opt. Lett. 31, 3312 (2006).
[Crossref] [PubMed]

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, “Soliton Topology versus Discrete Symmetry in Optical Lattices,” Phys. Rev. Lett. 95, 123 902 (2005).
[Crossref]

Y. V. Kartashov, R. Carretero-González, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Multipole-mode solitons in Bessel optical lattices,” Opt. Express 13, 10 703 (2005).
[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable Ring-Profile Vortex Solitons in Bessel Optical Lattices,” Phys. Rev. Lett. 94, 043 902 (2005).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable Spatiotemporal Solitons in Bessel Optical Lattices,” Phys. Rev. Lett. 95, 023 902 (2005).
[Crossref]

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical Vortices and Vortex Solitons,” Prog. Opt. 47, 291 (2005).
[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary Solitons in Bessel Optical Lattices,” Phys. Rev. Lett. 93, 093 904 (2004).
[Crossref]

Y. V. Kartashov, A. Egorov, V. Vysloukh, and L. Torner, “Rotary dipole-mode solitons in Bessel optical lattices,” J. Opt. B: Quantum Semiclass. Opt. 6, 444 (2004).
[Crossref]

D. Mihalache, D. Mazilu, L.-C. Crasovan, B. A. Malomed, F. Lederer, and L. Torner, “Robust soliton clusters in media with competing cubic and quintic nonlinearities,” Phys. Rev. E 68, 046 612 (2003).
[Crossref]

L.-C. Crasovan, Y. V. Kartashov, D. Mihalache, L. Torner, Y. S. Kivshar, and V. M. Pérez-García, “Soliton molecules: Robust clusters of spatiotemporal optical solitons,” Phys. Rev. E 67, 046 610 (2003).
[Crossref]

Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, “Robust Propagation of Two-Color Soliton Clusters Supported by Competing Nonlinearities,” Phys. Rev. Lett. 89, 273 902 (2002).
[Crossref]

Turunen, J.

Vasara, A.

Vogels, J. M.

J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, “Observation of Vortex Lattices in Bose-Einstein Condensates,” Science 292, 476 (2001).
[Crossref] [PubMed]

Vuong, L. T.

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and Stability of Necklace Beams in Kerr Media,” Phys. Rev. Lett. 99, 133 902 (2007).
[Crossref]

Vysloukh, V.

Y. V. Kartashov, A. Egorov, V. Vysloukh, and L. Torner, “Rotary dipole-mode solitons in Bessel optical lattices,” J. Opt. B: Quantum Semiclass. Opt. 6, 444 (2004).
[Crossref]

Vysloukh, V. A.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable Ring-Profile Vortex Solitons in Bessel Optical Lattices,” Phys. Rev. Lett. 94, 043 902 (2005).
[Crossref]

Y. V. Kartashov, R. Carretero-González, B. A. Malomed, V. A. Vysloukh, and L. Torner, “Multipole-mode solitons in Bessel optical lattices,” Opt. Express 13, 10 703 (2005).
[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary Solitons in Bessel Optical Lattices,” Phys. Rev. Lett. 93, 093 904 (2004).
[Crossref]

Wang, H. Z.

Y. J. He, H. H. Fan, J. W. Dong, and H. Z. Wang, “Self-trapped spatiotemporal necklace-ring solitons in the Ginzburg-Landau equation,” Phys. Rev. E 74, 016 611 (2006).
[Crossref]

Wang, X.

X. Wang, Z. Chen, and J. Yang, “Guiding light in optically induced ring lattices with a low-refractive-index core,” Opt. Lett. 31, 1887 (2006).
[Crossref] [PubMed]

X. Wang, Z. Chen, and P. G. Kevrekidis, “Observation of Discrete Solitons and Soliton Rotation in Optically Induced Periodic Ring Lattices,” Phys. Rev. Lett. 96, 083 904 (2006).

Widera, A.

O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hnsch, and I. Bloch, “Controlled collisions for multi-particle entanglement of optically trapped atoms,” Nature 425, 937 (2003).
[Crossref] [PubMed]

Xu, Z.

Yang, J.

X. Wang, Z. Chen, and J. Yang, “Guiding light in optically induced ring lattices with a low-refractive-index core,” Opt. Lett. 31, 1887 (2006).
[Crossref] [PubMed]

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike Solitons in Optically Induced Photonic Lattices,” Phys. Rev. Lett. 94, 113 902 (2005).
[Crossref]

J. Yang, “Stability of vortex solitons in a photorefractive optical lattice,” N. J. Phys. 6, 47 (2004).
[Crossref]

J. Yang and Z. H. Musslimani, “Fundamental and vortex solitons in a two-dimensional optical lattice,” Opt. Lett. 28, 2094 (2003).
[Crossref] [PubMed]

Yin, J.

J. Yin, W. Gao, and Y. Zhu, “Generation of dark hollow beams and their applications,” Prog. Opt. 45, 119 (2003).
[Crossref]

Zhu, Y.

J. Yin, W. Gao, and Y. Zhu, “Generation of dark hollow beams and their applications,” Prog. Opt. 45, 119 (2003).
[Crossref]

J. Opt. B: Quantum Semiclass. Opt. (1)

Y. V. Kartashov, A. Egorov, V. Vysloukh, and L. Torner, “Rotary dipole-mode solitons in Bessel optical lattices,” J. Opt. B: Quantum Semiclass. Opt. 6, 444 (2004).
[Crossref]

J. Opt. Soc. Am. A (1)

N. J. Phys. (1)

J. Yang, “Stability of vortex solitons in a photorefractive optical lattice,” N. J. Phys. 6, 47 (2004).
[Crossref]

Nature (2)

O. Mandel, M. Greiner, A. Widera, T. Rom, T. W. Hnsch, and I. Bloch, “Controlled collisions for multi-particle entanglement of optically trapped atoms,” Nature 425, 937 (2003).
[Crossref] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, “Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices,” Nature (London)  422, 147 (2003).
[Crossref] [PubMed]

Opt. Commun. (1)

J. Arlt and K. Dholakia, “Generation of high-order Bessel beams by use of an axicon,” Opt. Commun. 177, 297 (2000).
[Crossref]

Opt. Express (3)

Opt. Lett. (4)

Phys. Rev. E (3)

Y. J. He, H. H. Fan, J. W. Dong, and H. Z. Wang, “Self-trapped spatiotemporal necklace-ring solitons in the Ginzburg-Landau equation,” Phys. Rev. E 74, 016 611 (2006).
[Crossref]

D. Mihalache, D. Mazilu, L.-C. Crasovan, B. A. Malomed, F. Lederer, and L. Torner, “Robust soliton clusters in media with competing cubic and quintic nonlinearities,” Phys. Rev. E 68, 046 612 (2003).
[Crossref]

L.-C. Crasovan, Y. V. Kartashov, D. Mihalache, L. Torner, Y. S. Kivshar, and V. M. Pérez-García, “Soliton molecules: Robust clusters of spatiotemporal optical solitons,” Phys. Rev. E 67, 046 610 (2003).
[Crossref]

Phys. Rev. Lett. (13)

J. Yang, I. Makasyuk, P. G. Kevrekidis, H. Martin, B. A. Malomed, D. J. Frantzeskakis, and Z. Chen, “Necklacelike Solitons in Optically Induced Photonic Lattices,” Phys. Rev. Lett. 94, 113 902 (2005).
[Crossref]

A. S. Desyatnikov and Y. S. Kivshar, “Rotating Optical Soliton Clusters,” Phys. Rev. Lett. 88, 053 901 (2002).
[Crossref]

Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, “Robust Propagation of Two-Color Soliton Clusters Supported by Competing Nonlinearities,” Phys. Rev. Lett. 89, 273 902 (2002).
[Crossref]

M. SoljaÇić, S. Sears, and M. Segev, “Self-Trapping of Necklace Beams in Self-Focusing Kerr Media,” Phys. Rev. Lett. 81, 4851 (1998).
[Crossref]

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and Stability of Necklace Beams in Kerr Media,” Phys. Rev. Lett. 99, 133 902 (2007).
[Crossref]

A. S. Desyatnikov and Y. S. Kivshar, “Necklace-Ring Vector Solitons,” Phys. Rev. Lett. 87, 033 901 (2001).
[Crossref]

M. SoljaÇić and M. Segev, “Integer and Fractional Angular Momentum Borne on Self-Trapped Necklace-Ring Beams,” Phys. Rev. Lett. 86, 420 (2001).
[Crossref] [PubMed]

X. Wang, Z. Chen, and P. G. Kevrekidis, “Observation of Discrete Solitons and Soliton Rotation in Optically Induced Periodic Ring Lattices,” Phys. Rev. Lett. 96, 083 904 (2006).

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, “Observation of Discrete Vortex Solitons in Optically Induced Photonic Lattices,” Phys. Rev. Lett. 92, 123 903 (2004).
[Crossref]

D. Mihalache, D. Mazilu, F. Lederer, B. A. Malomed, Y. V. Kartashov, L.-C. Crasovan, and L. Torner, “Stable Spatiotemporal Solitons in Bessel Optical Lattices,” Phys. Rev. Lett. 95, 023 902 (2005).
[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Rotary Solitons in Bessel Optical Lattices,” Phys. Rev. Lett. 93, 093 904 (2004).
[Crossref]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Stable Ring-Profile Vortex Solitons in Bessel Optical Lattices,” Phys. Rev. Lett. 94, 043 902 (2005).
[Crossref]

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, “Soliton Topology versus Discrete Symmetry in Optical Lattices,” Phys. Rev. Lett. 95, 123 902 (2005).
[Crossref]

Prog. Opt. (2)

A. S. Desyatnikov, Y. S. Kivshar, and L. Torner, “Optical Vortices and Vortex Solitons,” Prog. Opt. 47, 291 (2005).
[Crossref]

J. Yin, W. Gao, and Y. Zhu, “Generation of dark hollow beams and their applications,” Prog. Opt. 45, 119 (2003).
[Crossref]

Science (1)

J. R. Abo-Shaeer, C. Raman, J. M. Vogels, and W. Ketterle, “Observation of Vortex Lattices in Bose-Einstein Condensates,” Science 292, 476 (2001).
[Crossref] [PubMed]

Other (2)

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, San Diego,Calif., 2003).

Y. Silberberg and G. I. Stegeman, Spatial Solitons (Springer, New York, 2001).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Power and instability growth of 8-“pearl” necklace solitons residing on the first ring of the 1-order Bessel lattice vs b at p=30. (b, c) Profiles of solitons with p=30,b=0.6 in (b) and p=30,b=7.5 in (c). (d) Superposition contour of lattice and necklace soliton shown in (c). (e,f) Propagation simulation of soliton shown in (c) at z=0 and z=256 respectively. White noise with variance |σnoise |=0.1 was added into the initial input.

Fig. 2.
Fig. 2.

Profiles of necklace solitons. (a) 20-“pearls”, p=30,b=2.0 residing on the second ring of lattice. (b) 14-“pearls”, p=40,b=1.5 residing on the third ring of lattice. (c) 44-“pearls”, p=40,b=1.5 residing on the third ring of lattice. (d) 32-“pearls”, p=55,b=1.1 residing on the fourth ring of lattice.

Fig. 3.
Fig. 3.

(a) Existence and instability (shaded) domains of 44-“pearl” necklace solitons. (b) The imaginary part of the perturbation growth rate vs propagation constant at p=40. (c, d) Stable propagation of the necklace soliton shown in Fig. 2(c). z=0 in (c) and 256 in (d). White noise with variance |σnoise |=0.1 was added into the initial input.

Fig. 4.
Fig. 4.

(a) Phase structure of 32-“pearl” soliton [Fig. 2(d)] carrying global angular momentum in the form of exp(4). (b–d) Stable clockwise rotation of the 32-“pearl” soliton. z=0 in (b), 128 in (c) and 256 in (d). White noise with variance |σnoise |=0.1 was added into the initial input.

Fig. 5.
Fig. 5.

(a–c) Contour plots of ring solitons supported by 1-order Bessel lattice. The ring solitons reside on the second ring of lattice in (a),(b) and third ring in (c). (a) b=1.2, p=20. (b) b=0.79, p=20. (c) b=1.7, p=35. (d) Existence and instability (shaded) domains in the p,b plane for the ring solitons residing on the second ring of lattice.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

i A z + 1 2 ( 2 A x 2 + 2 A y 2 ) A 2 A + p R ( x , y ) A = 0
( 2 q x 2 + 2 q y 2 ) 2 q 3 2 bq + 2 pRq = 0
λ u = 1 2 ( 2 u x 2 + 2 u y 2 ) + q 2 ( 2 u + v ) pRu + bu
λ v = 1 2 ( 2 v x 2 + 2 v y 2 ) q 2 ( 2 v + u ) + pRv bv

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